Solve for $x$ and $y$ using elimination. ${-6x-y = -33}$ ${-5x+y = -22}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-11x = -55$ $\dfrac{-11x}{{-11}} = \dfrac{-55}{{-11}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-6x-y = -33}\thinspace$ to find $y$ ${-6}{(5)}{ - y = -33}$ $-30-y = -33$ $-30{+30} - y = -33{+30}$ $-y = -3$ $\dfrac{-y}{{-1}} = \dfrac{-3}{{-1}}$ ${y = 3}$ You can also plug ${x = 5}$ into $\thinspace {-5x+y = -22}\thinspace$ and get the same answer for $y$ : ${-5}{(5)}{ + y = -22}$ ${y = 3}$